Phase synchronization with type-II intermittency in chaotic oscillators

Chaotic behaviors of operational amplifiers

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

Current reversal with type-I intermittency in deterministic inertia ratchets

The intermittency is investigated when the current reversal occurs in a deterministic inertia ratchet system. To determine which type the intermittency belongs to, we obtain the return map of velocities of particle by using stroboscopic recordings, and by numerically calculating the distribution of the average laminar length <l>. The distribution follows the scaling law of <l> proportional to epsilon(-1/2), the characteristic relation of type-I intermittency.

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

Phase synchronization in coupled chaotic oscillators with time delay

The phase synchronization (PS) of two Rössler oscillators with time-delayed signal coupling is studied. We find that time delay can always lead to PS even when the delay is very long. Moreover, with the increase of time delay, the coupling strength at the transition to PS undergoes a nearly periodic wave distribution. At some fixed time-delayed signal coupling, a PS region is followed by a non-PS region when the coupling strength increases. However, an increase of the coupling leads to the PS state again. This phenomenon occurs in systems with a relatively large PS transition point.

Phase synchronization in bidirectionally coupled optothermal devices

We present the experimental observation of phase synchronization transitions in the bidirectional coupling of chaotic and nonchaotic oscillators. A variety of transitions are characterized and compared to numerical simulations of a time delayed model. The characteristic 2pi phase jumps usually appear during the transitions, specially in those clearly associated with a saddle-node bifurcation. The study is done with pairs of optothermal oscillators linearly coupled by heat transfer.

Routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators

We study the transition route to complete synchronization through phase synchronization in generic coupled nonidentical chaotic oscillators. Through numerical studies, two routes are found, i.e., one, via lag synchronization, the other, via the intermittent chaotic burst state without lag synchronization. We claim that these two routes are universal. As evidence, we analyze several examples on the basis of the conventional theory of intermittency in the presence of noise.

n:m phase synchronization with mutual coupling phase signals

We generalize the n:m phase synchronization between two chaotic oscillators by mutual coupling phase signals. To characterize this phenomenon, we use two coupled oscillators to demonstrate their phase synchronization with amplitudes practically noncorrelated. We take the 1:1 phase synchronization as an example to show the properties of mean frequencies, mean phase difference, and Lyapunov exponents at various values of coupling strength. The phase difference increases with 2pi phase slips below the transition. The scaling rules of the slip near and away from the transition are studied. Furthermore, we demonstrate the transition to a variety of n:m phase synchronizations and analyze the corresponding coupling dynamics. (c) 2002 American Institute of Physics.

Phase synchronization in coupled Nd:YAG lasers

We investigate experimentally the transition to phase synchronization in coupled Nd:YAG lasers. As the coupling strength increases, the phase difference of two chaotic laser outputs develops from nonsynchronous to a phase-synchronous state via +/-2pi phase jumps. We analyze this transition.

Intermittent phase synchronization of coupled spatiotemporal chaotic systems

Phase synchronization is studied with a discrete system formed by two coupled map lattices, in which phases are measured in two-dimensional vectors. Simulation results show that by imposing external coupling between the two lattices, phase synchronization can be found in all two-dimensional phase planes between them. When the system is approaching the phase synchronizing state, unstable phase synchronization is observed. This is referred to as intermittent phase synchronization that appears when the trajectories on two interacting phase planes have opposite directions of rotation but with only a small phase difference. The intermittent phase synchronization could also be observed in coupled autonomous systems with diffusive attractors although their phase concepts are inconsistent. Our results show that the intermittent phase synchronization of both discrete and autonomous systems relates to the diffusion or the complexity of the attractors.